Initial Problem

Start: start
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: eval, start
Transitions:
t₀: eval(X₀, X₁, X₂) → eval(X₀-1, X₁, X₂) :|: 1 ≤ X₀ ∧ 1+X₂ ≤ X₀+X₁ ∧ 0 ≤ X₂
t₁: eval(X₀, X₁, X₂) → eval(X₀, X₁-1, X₂) :|: 1+X₂ ≤ X₀+X₁ ∧ 1 ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₂
t₂: eval(X₀, X₁, X₂) → eval(X₀, X₁, X₂) :|: 1+X₂ ≤ X₀+X₁ ∧ X₀ ≤ 0 ∧ X₁ ≤ 0 ∧ 0 ≤ X₂
t₃: start(X₀, X₁, X₂) → eval(X₀, X₁, X₂)

Preprocessing

Cut unsatisfiable transition [t₂: eval→eval]

Problem after Preprocessing

Start: start
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: eval, start
Transitions:
t₀: eval(X₀, X₁, X₂) → eval(X₀-1, X₁, X₂) :|: 1 ≤ X₀ ∧ 1+X₂ ≤ X₀+X₁ ∧ 0 ≤ X₂
t₁: eval(X₀, X₁, X₂) → eval(X₀, X₁-1, X₂) :|: 1+X₂ ≤ X₀+X₁ ∧ 1 ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₂
t₃: start(X₀, X₁, X₂) → eval(X₀, X₁, X₂)

MPRF for transition t₀: eval(X₀, X₁, X₂) → eval(X₀-1, X₁, X₂) :|: 1 ≤ X₀ ∧ 1+X₂ ≤ X₀+X₁ ∧ 0 ≤ X₂ of depth 1:

new bound:

X₀ {O(n)}

• eval: [X₀]

MPRF for transition t₁: eval(X₀, X₁, X₂) → eval(X₀, X₁-1, X₂) :|: 1+X₂ ≤ X₀+X₁ ∧ 1 ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₂ of depth 1:

new bound:

X₁ {O(n)}

• eval: [X₁]

All Bounds

Timebounds

Overall timebound:X₀+X₁+1 {O(n)}
t₀: X₀ {O(n)}
t₁: X₁ {O(n)}
t₃: 1 {O(1)}

Costbounds

Overall costbound: X₀+X₁+1 {O(n)}
t₀: X₀ {O(n)}
t₁: X₁ {O(n)}
t₃: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₁, X₀: 2⋅X₀ {O(n)}
t₁, X₁: 2⋅X₁ {O(n)}
t₁, X₂: 2⋅X₂ {O(n)}
t₃, X₀: X₀ {O(n)}
t₃, X₁: X₁ {O(n)}
t₃, X₂: X₂ {O(n)}